# Johannes Rydberg

**
SWEDISH MATHEMATICIAN AND PHYSICIST
1854–1919
**

Johannes Robert Rydberg was born in Halmstad, Sweden, on November 8, 1854. His father, Sven, was a local merchant and minor shipowner who died when Rydberg was young. Rydberg attended the local gymnasium (or high school) in Halmstad and studied languages, religion and philosophy, history and geography, and natural history, along with mathematics and physics. Although a good all-around student, Rydberg chose to pursue mathematics at the university.

He entered the University of Lund in the autumn of 1873, and it is fair to say that he never left. He received his doctorate in mathematics from that institute in 1879 and was appointed a teacher of mathematics there in 1881. But in 1876 Rydberg was also appointed as a teaching assistant at Lund's physics institute. His experimental study on friction electricity led to a position as a teacher of physics in 1882.

As a physicist and mathematician, Rydberg was driven by a desire to
understand the basic physical laws behind the Periodic Table. He set out
to
find order in the mass of
**
spectroscopic
**
data that was then available. Atomic spectra had been used to
characterize minerals and to ascertain the chemical composition of distant
stars, but the underlying order was not apparent. While various
spectroscopists had noted that line spectra could be discriminated into
"sharp," "principal," and
"diffuse" patterns, a guiding relationship between the lines
had not yet emerged.

Rydberg decided to use the wave number as a measure of frequency in his
calculations. A wave number is the reciprocal of the wavelength, and,
although Rydberg did not know this at the time, it is directly related to
energy, unlike the more common wavelength that bears an inverse
relationship. Having made this change, patterns began to emerge in the
data with a particular series of lines for any atom leading to a
**
hyperbolic relationship
**
. Indeed, the same relationship was observed for all the different
spectroscopic series and for different elements.

Rydberg devised the formula

*
n = n
*
_{
0
}
−
*
N
*
_{
0
}
/(
*
m + m
*
′)
^{
2
}

and was testing it against the data when the Swiss mathematician and
physicist Johann Balmer published his result for hydrogen atoms,
wavelength =
*
hm
*
^{
2
}
/(
*
m
*
^{
2
}
− 4). Rydberg quickly realized that this was just a special case
of his formula with
*
m
*
′ = 0 and
*
N
*
_{
0
}
= 4
*
n
*
_{
0
}
and that
*
N
*
_{
0
}
must be a universal constant. Using this information, Rydberg was able to
show that his equation was more general and published it in 1890, well
before the spectroscopic series discovered by Balmer, the American
Theodore Lyman, or the German Friedrich Paschen provided experimental
confirmation.

The formula is now written as

1/λ = R
_{
H
}
(1/n
_{
1
}
^{
2
}
− 1/n
_{
2
}
^{
2
}
)

where both values of
*
n
*
are integers, but
*
n
*
_{
2
}
*
n
*
_{
1
}
. The term
*
N
*
_{
0
}
has been replaced by
*
R
*
_{
H
}
, the so-called Rydberg constant. It is a fundamental constant of nature
and a measure of the strength of the
**
nuclear
**
-electron interaction in atoms.

**
SEE ALSO
**
Balmer, Johann Jakob
;
Spectroscopy
.

*
Todd W. Whitcombe
*

## Bibliography

Bohr, Niels (1954). "Rydberg's Discovery of the Spectral
Laws."
*
Proceedings of the Rydberg Centennial Conference on Atomic Spectroscopy,
Acta Universitatis lundensis
*
50: 15–21.

Pauli, Wolfgang (1954). "Rydberg and the Periodic System of the
Elements."
*
Proceedings of the Rydberg Centennial Conference on Atomic Spectroscopy,
Acta Universitatis lundensis
*
50: 22–26.

### Internet Resources

O'Connor, J. J., and Robertson, E. F. "Johannes Robert Rydberg." Available from http://www-gap.dcs.st-and.ac.uk/,history/Mathematicians/Rydberg.html .

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